STPZ at Monotonic Loading

Abstract

The Simplified Theory of Plastic Zones (STPZ) is primarily intended to estimate stresses and strains at variable load. However, the basic idea of the STPZ, based on Zarka’s method, is easier to present initially for monotonic loading. A bilinear stress–strain curve, that is, linear kinematic hardening, is initially assumed as well as constant material data that do not change with temperature during thermal loading. After introducing a transformed internal variable, the yield criterion is reformulated. A modified elastic material law is obtained, and its modified elastic material parameters are identified. Furthermore, the transformed internal variable is used to define initial strains, which are estimated in a suitable manner and can be applied as a modified loading in a modified elastic analysis. The results in terms of residual quantities can be superimposed on the results of a fictitious elastic analysis to get an approximation of the elastic-plastic solution, which in turn is the starting point for an iterative improvement. Examples illustrate the calculation process and the quality of the approximate solution obtained, along with the computational burden involved. Chapter 4 then presents an extension to cyclic loading, Chap. 5 to temperature-dependent material data, and Chap. 7 to multilinear stress–strain behavior.